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October 17th, 2012, 12:53 AM  #1 
Senior Member Joined: Sep 2012 Posts: 112 Thanks: 0  application of differentiation in economics
A monopolist produces x units of a commodity at a total cost of ax^2+bx+c and the demand law for the same is given by p= QRx, where Q and R constants. A tax of Rs.K per unit is levied by the government. The manufacturer adds the tax to his cost. (a) find the price and the output both before and after tax. (b) show that the tax brings in maximum return when K=(Qb)/2 I could solve the 1st question i.e. (a). But I don't know how to solve (b). Please help. 
October 17th, 2012, 09:39 AM  #2 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: application of differentiation in economics
Tax is maximized when the derivative of tax revenue is 0. First solve for tax revenue, then differentiate. Next set this equal to zero and solve. Finally, substitute back into the original.

October 17th, 2012, 10:00 PM  #3  
Senior Member Joined: Sep 2012 Posts: 112 Thanks: 0  Re: application of differentiation in economics Quote:
 
October 18th, 2012, 06:25 AM  #4 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: application of differentiation in economics
Yes.

October 28th, 2012, 08:37 AM  #5  
Senior Member Joined: Sep 2012 Posts: 112 Thanks: 0  Re: application of differentiation in economics Quote:
 

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